A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes
Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithms for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Biological and Environmental Research (BER)
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1351231
- Alternate ID(s):
- OSTI ID: 1416381
- Report Number(s):
- LA-UR-16-28346
- Journal Information:
- Advances in Water Resources, Vol. 104; ISSN 0309-1708
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils
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journal | June 2019 |
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